Question

Let $p,q$ be irrational numbers, such that, $p^2$ and $q^2$ are relatively prime. Show that $\sqrt{pq}$ is also irrational.

score 1.8k · Answer 1 · 2016-09-13 00:11:24

1.8k

Views

Let $p,q$ be irrational numbers, such that, $p^2$ and $q^2$ are relatively prime. Show that $\sqrt{pq}$ is also irrational.

Published on 13 Sep 2016 - 0:11

score 102 · Answer 2 · 2016-09-13 20:08:59

102

Views

Rational root of the sum of two squares

Published on 13 Sep 2016 - 20:08

score 171 · Answer 3 · 2016-09-14 02:41:30

171

Views

Rational and irrational sequences

Published on 14 Sep 2016 - 2:41

score 692 · Answer 4 · 2016-09-16 01:43:23

692

Views

Are all non-irrational numbers rational?

Published on 16 Sep 2016 - 1:43

score 287 · Answer 5 · 2016-09-18 12:34:39

287

Views

How can I deduce that this is always an integer?

Published on 18 Sep 2016 - 12:34

score 4.2k · Answer 6 · 2016-09-19 09:49:36

4.2k

Views

How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?

Published on 19 Sep 2016 - 9:49

score 178 · Answer 7 · 2016-09-19 19:25:44

178

Views

Will irrational exponents always yield irrational results?

Published on 19 Sep 2016 - 19:25

score 1.4k · Answer 8 · 2016-09-20 00:46:40

1.4k

Views

What relations define a mapping?

Published on 20 Sep 2016 - 0:46

score 99 · Answer 9 · 2016-09-21 01:24:31

99

Views

Is this a valid proof for proving $ 2 + \sqrt{2}$ is irrational?

Published on 21 Sep 2016 - 1:24

score 10.1k · Answer 10 · 2016-09-23 04:31:31

10.1k

Views

Prove $\sqrt{3} + \sqrt{5}$ is irrational

Published on 23 Sep 2016 - 4:31

score 745 · Answer 11 · 2016-09-23 06:21:03

745

Views

How to show that $a\sqrt 6 + b \sqrt 3 + c \sqrt 2$ is irrational where $a,b,c \in \mathbb{Q}$

Published on 23 Sep 2016 - 6:21

score 495 · Answer 12 · 2016-09-23 14:18:02

495

Views

Irrational and rational sequence

Published on 23 Sep 2016 - 14:18

score 226 · Answer 13 · 2026-03-30 01:28:41

226

Views

How can $(\sqrt n)^2$ for $n$ not a perfect square be an integer?

Published on 30 Mar 2026 - 1:28

score 1.9k · Answer 14 · 2026-03-29 16:56:06

1.9k

Views

Do there exist numbers normal in every base except for one?

Published on 29 Mar 2026 - 16:56

score 7.7k · Answer 15 · 2016-09-27 00:21:12

7.7k

Views

Prove or disprove that there is a rational number $x$ and an irrational number $y$ such that $x^y$ is irrational

Published on 27 Sep 2016 - 0:21

List Question

Let $p,q$ be irrational numbers, such that, $p^2$ and $q^2$ are relatively prime. Show that $\sqrt{pq}$ is also irrational.

Rational root of the sum of two squares

Rational and irrational sequences

Are all non-irrational numbers rational?

How can I deduce that this is always an integer?

How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?

Will irrational exponents always yield irrational results?

What relations define a mapping?

Is this a valid proof for proving $ 2 + \sqrt{2}$ is irrational?

Prove $\sqrt{3} + \sqrt{5}$ is irrational

How to show that $a\sqrt 6 + b \sqrt 3 + c \sqrt 2$ is irrational where $a,b,c \in \mathbb{Q}$

Irrational and rational sequence

How can $(\sqrt n)^2$ for $n$ not a perfect square be an integer?

Do there exist numbers normal in every base except for one?

Prove or disprove that there is a rational number $x$ and an irrational number $y$ such that $x^y$ is irrational

Trending Questions

Popular # Hahtags

Popular Questions